UX is an acronym for User Experience. A UX designer is a person who helps software developers design the user interface of their product or web resource in a way that makes it easier to use for the end users. This term also applies to physical devices, but is getting very popular in the software development and web design fields.
The is no well-defined list of things a UX designer does, this depends on the company and specific project. As a rule, the goal of a UX project is to improve the product usability, make it more appealing, help the users complete their tasks easier and faster, make the user interface more useful, etc.